应用数学和力学

1984 Vol. 5, No. 4

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Time-Independent Anisotropic Plastic Behavior by Mechanical Subelement Models

Theodore H. H. Pian

1984, 5(4): 461-470.

Abstract(1756) PDF(483)

Abstract:
The paper describes a procedure for modelling the aniso-tropic elastic-plastic behavior of metals in plane stress state by the mechanical sub-layer model. In this model the stress-strain curves along the longitudinal and transverse directions are represented by short smooth segments which are consid...

Wave and Earthquake Effects on Axisymmetric Offshore Structures

Professor Michael Isaacson, Wu Song-ren

1984, 5(4): 471-480.

Abstract(1826) PDF(532)

Abstract:
Vertical axisymmetric structures have found a variety of applications in offshore engineering, including oil storage tanks, production platforms and so on. The present paper describes an efficient calculation procedure for determining the interaction of such structures with the surrounding ocean. In...

Some Applications of the Singular Perturbation Method to the Bending Problems of Thin Plates and Shells

Chou Huan-wen

1984, 5(4): 481-488.

Abstract(1642) PDF(663)

Abstract:
This paper presents a review which tackles some nonlinear bending problems of plates and shells in a unified way by means of the technique of undetermined small parameters.

Load Supporting Prefabricated Wall Reinforced by a Frame

Chang Fo-van, Yan Kun-fu

1984, 5(4): 489-498.

Abstract(1802) PDF(520)

Abstract:
This load supporting prefabricated wall consists of a thin plate reinforced along its boundaries by a frame. With the loads acting on the frame, the plate has its boundary conditions defined neither by forces nor by displacements. On the basis of satisfying the biharmonic equation of the stress func...

The Generalized Boussinesq Equations and Obliquely Interacting Solitary Waves in a Stratified Fluid

Dai Shi-qiang

1984, 5(4): 499-509.

Abstract(1766) PDF(771)

Abstract:
In this paper, on the basis of Boussinesq's shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, gi...

On the Heat Conduction Problems and a Design Principle for Plasma Arc Furnace

Rong Sheng

1984, 5(4): 511-517.

Abstract(1876) PDF(627)

Abstract:
In this paper a plane heat conduction problem with variable coefficients of heat conductivity K(T) is analysed with given electric power supplied to the plasma arc. The governing equation for unknown temperature distribution is a nonlinear one with a δ function as its nonhomogeneous term. To make th...

Pulsatile Flow in Arteries with External Restraint of Visco-Elastic Tissue

Liu Zhao-rong

1984, 5(4): 519-526.

Abstract(2011) PDF(429)

Abstract:
The presence of a longitudinal constraint must be conceived physiologically as due largely to the connective tissue attachments on the outside of the artery. Living tissues are yisco-elastic bodies. In order to analyse the effect of external visco-elastic tissue to pulsatile flow in arteries, in thi...

On Singular Perturbation Method of Perturbed Bifurcation Problems

Chu Zheng-you, Cheng Chang-jun

1984, 5(4): 527-534.

Abstract(1917) PDF(425)

Abstract:
In this paper, the general mathematical principle is over-all explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, λ=0,δ=0, by means of singular perturbation method. Si...

Hopf Bifurcation Phenomenon in Catalytic Reaction

Liu Zheng-rong, Lin Chang

1984, 5(4): 535-540.

Abstract(1928) PDF(469)

Abstract:
In this paper, we intend to discuss Hopf bifurcation phenomenon under the effect of the periddic small perturbation on local temperature fluctuations (flikeringiy) phenomenon of catalytic reaction. With the obtained results, we expect to provide basis for selecting reaction parameters.

The Fission of Spectrum Line of Monochoromatic Elastic Wave

Shen Hui-chuan

1984, 5(4): 541-551.

Abstract(1880) PDF(668)

Abstract:
On the basis of the anology with quantum electrodynamics, Dirac equation of elastic wave-phonon is developed and the fission of spectrum line of monochoromatic elastic wave under the action of an external field is studied in this paper.

Solution of Non-Linear Heat Conduction Equation and image Method

Zhang Guan-ren

1984, 5(4): 553-559.

Abstract(1917) PDF(475)

Abstract:
In this paper, the author proves that, for a nonlinear heat conduction equation, there is no discontinuous solution. Some methods of solution for a nonlinear conduction equation are depicted. For a plane interface, the reflection and transmission of a heat wave are given by the method of images. The...

Fixed Point Theorems of Random Set-Valued Mappings and Their Applications

Ding Xie-ping

1984, 5(4): 561-575.

Abstract(1905) PDF(721)

Abstract:
In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and diffe...

On the General Equations of Axisymmetric Problems of Ideal Plasticity

Shen Hui-shen

1984, 5(4): 577-582.

Abstract(1772) PDF(584)

Abstract:
In this paper, introducing a velocity potential, we reduce the fundamental equations of axisymmetric problems of ideal plasticity to two nonlinear partical differential equations. Front these equations we discuss compatibility of Harr-Kármán hypothesis with von Mises yield criterion and the associat...

The Strain Energy Criterion of Mixed-Mode Brittle Fracture

Lin Bai-song

1984, 5(4): 583-588.

Abstract(1992) PDF(538)

Abstract:
In this paper, we proposed a new cr tenon or mixea-moae brittle fracture, i.e., the strain energy criterion, which can be stated as (K_Ⅰ/K_Ⅰc)² +(K_Ⅱ/K_Ⅱc)²+(K_Ⅲ/K_Ⅲc)²=1. This criterion is shown to be in good agreement with known experimental data.In this paper, an experimental criterion:(K_Ⅰ/K_Ⅰc)^m+(K_Ⅱ/K_Ⅱ...

On the Finite Displacement Problem of a Hollow Cylinder under Internal and External Pressures

Huang Ze-yan

1984, 5(4): 589-602.

Abstract(1801) PDF(747)

Abstract:
Using the method of successive approximations we find of this boundary-value problem the first-and second-order solutions. And then we obtain the formulae in the second approximation for the displacement, strain, and stress fields. Also, our results show that after deformation (i) a cross-section of...